PageRank Optimization in Polynomial Time by Stochastic Shortest Path Reformulation

  • Balázs Csanád Csáji
  • Raphaël M. Jungers
  • Vincent D. Blondel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6331)


The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts – including ranking websites – and can be interpreted as the average portion of time spent at the node by an infinite random walk. We consider the problem of maximizing the PageRank of a node by selecting some of the edges from a set of edges that are under our control. By applying results from Markov decision theory, we show that an optimal solution to this problem can be found in polynomial time. It also indicates that the provided reformulation is well-suited for reinforcement learning algorithms. Finally, we show that, under the slight modification for which we are given mutually exclusive pairs of edges, the problem of PageRank optimization becomes NP-hard.


PageRank graphs complexity Markov decision processes 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Balázs Csanád Csáji
    • 1
    • 2
  • Raphaël M. Jungers
    • 3
    • 4
  • Vincent D. Blondel
    • 4
  1. 1.Department of Electrical and Electronic Engineering, School of EngineeringThe University of MelbourneAustralia
  2. 2.Computer and Automation Research InstituteHungarian Academy of Sciences 
  3. 3.Lab. for Information and Decision SystemsMassachusetts Institute of Technology 
  4. 4.Department of Mathematical EngineeringUniversité catholique de LouvainBelgium

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